The 25-year-old becomes the Baggies third signing of the current transfer window, and the second goalkeeper to arrive at the Hawthorns ahead of the 2018/19 campaign.
Bond has signed a two-year contract with the club and will join as a free agent after a three-year spell at Reading came to an end this summer, having made just 14 appearances for the Royals across all competitions.
"This is a Premier League club and that’s what we’ve got to concentrate on - getting ourselves back up there," Bond told the club's official website. "The facilities are great, the people are great. The Championship is a tough league but I believe it’s an exciting season ahead."
Goalkeepers were high on the agenda for West Brom this summer following the departure of Ben Foster, who has returned to the Premier League with Watford, and Boaz Myhill - now a free agent.
Former Aston Villa loanee Sam Johnstone has joined the club for just over £6.5m after an agreement was reached with Manchester United, while defender Kyle Bartley remains their only outfield signing so far this summer.
There are concerns that a number of key first team players will also leave ahead of the new campaign, with Salomón Rondón and Matt Phillips likely to return to the Premier League this summer.